hartley
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constexpr Complex laplace(Complex (*f)(Complex), const Complex &z) noexcept
Performs the Hartley integral transform [1] of a complex function.
Parameters
Returns
- type Complex
A complex number.
The Hartley transform performs the following integral transform on a function \(f\):
\[\DeclareMathOperator\cas{cas}
H(\omega) = \{\mathcal{H}f\}(\omega) = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}f(t)\cas(\omega t)dt\]
where \(\DeclareMathOperator\cas{cas} \cas(t)\) is defined as:
\[\DeclareMathOperator\cas{cas}
\cas(t) = \cos(t) + \sin(t)\]
Example
auto fn = [](Complex t) { return exp(-t * t); };
Complex z = 1;
std::cout << hartley(fn, z) << "\n";
Output:
0.550782 + 0j // True result: 0.550695 + 0j
References